Download Take Home Final

Name:________________________
Math 311 – Fall 2008
Take Home Final
Instructions: Because this is a take home final and calculators are allowed as well as
your books and notes, it is even more important that you show all your work. Fractions
and decimals need to be worked using fractions or decimals respectively, and work for
LCD’s, building higher terms and long division and multiplication must always be
shown. You are allowed to use any resource except the help of another person. This test
is due on Wednesday, December 17, 2008. It needs to be handed in prior to the start of
the in-class portion of the final. If it is not received by the end of class and prior to the
start of the in-class portion, it will not be accepted. Good luck!
1.
a)
Write the prime factorization of the following numbers. Write the final answer
using exponential notation. Work must be shown.
20
b)
30
c)
24
2.
Find the LCD of
20, 30 & 24
Write the answer using exponential notation and then expand and simplify to a number.
3.
For 5/24, build the higher term so that the new denominator is 72.
4.
a)
What are all the factors each of the following.
72
b)
5.
Find the GCF of
6.
Give the following fraction in lowest terms. Show your work by canceling or
division.
72
108
Y. Butterworth
108
72 & 108
Take Home Final – Fall 2008
1
7.
Give both the improper fraction and the mixed number that represents the
shaded portion of the picture below.
Give the
8.
Write the following number in words. Watch spelling.
97.043
________________________________________________________________________
9.
Round
89.945
to each of the specified places.
a)
ones
b)
tenths _________________________________
c)
hundredths _____________________________
10.
Fill in the following table by making the conversions between decimals, fractions
and percentages. Work must always be shown – I have left room below the table
for that purpose.
Fraction
Decimal
Percent
4
/9
1.2
67.5%
11.
Simplify the following using order of operations. Do not use the distributive
property. Show your work for each step in the order of operations. Fractions stay in fractions
_________________________________
and decimals stay in decimals. You may use your calculator for calculating intermediate numbers,
like parentheses answers and product answers and quotient answers, but I must see intermediate
steps.
a)
(1/4)2  (2 ½  ¾) + 5/7
Y. Butterworth
b)
Take Home Final – Fall 2008
5 + 0.1(1.5  2.39)  0.1
2
c)
12.
5 + 9(3 + -1)  6
16  4  16
Find the
a)
b)
d)
area
perimeter
9(-1 + -8) + 34
2  3 5 + 4
of the patio with the following shape
90 feet
70 feet
60 feet
70 feet
40 feet
20 feet
13.
The following are word problems and therefore must show setup, an algebraic
equation and the solution to that equation solving the problem.
a)
Billy, June and Joe go to the movies. Each gets a ticket costing $6.50, drinks
costing $2.50 each, and Billy and June each have popcorn that costs $4.25 each,
Joe buys candy instead. If their total cost is $39, what was the cost of Joe’s
candy. This must be set up as a missing addend problem. Note that there are 3
instances of multiplication!
Y. Butterworth
Take Home Final – Fall 2008
3
b)
The difference in the elevation of Mt. Rushmore and Death Valley is 7524 feet,
and the elevation of Mt. Rushmore is 7242 feet, what is the elevation of Death
Valley. You must use a missing subtrahend setup.
c)
If the amount of rock in each bag is 3.25kg, how many bags weigh 45.5 kg? This
must be set up as a missing factor problem.
d)
The surface area of the room is 272 square feet. The paint that you have chosen
will need two coats, and it covers 150.5 square feet per gallon. How many
gallons will you have to buy in order to get two coats of paint on your walls?
e)
The train travels at 53 mph. How long will it take for the train to travel a distance
of 385 miles? (If necessary, round your answer to the nearest tenth of an hour.)
You must use a missing factor set-up.
Y. Butterworth
Take Home Final – Fall 2008
4
f)
Susan deposits $2500 in her account which earns 5 1/4 % simple annual interest.
If she leaves the money in the account for 2 ¾ years, how much interest should
she expect to make at the end of the time? There must be an equation, even if it is
very simple and all work must be shown with the decimal conversions.
EC)
Edgar and Sam each have a state quarter collection. Edgar has collected five less
than twice the number of quarters that Sam has collected. Between Sam and
Edgar they have $7 in quarters. How many quarters does each boy have?
14.
Translate each of the following into expressions or equations. If there is an
unknown number let that number be x. Do not simplify.
a)
The difference of some number and the product of fifteen and the sum of the
number and negative 9.
b)
The quotient of nine subtracted from some number and 27.
c)
Twenty-three less some number is equivalent to five more than twice that number.
d)
Three less than some number is divided by the product of the number and nine.
Y. Butterworth
Take Home Final – Fall 2008
5
15.
a)
Show all work for full credit. Change decimals to fractions and/or fractions to
decimals in order to compare. Too compare fractions build the higher terms and
compare numerators, or use the cross product trick shown in class.
Use <, > or = to compare.
- | - 95|
- ( - 45)
b)
| 918 |
| - 918 |
c)
5
/8
0.675
d)
0.885
0.889
e)
3
/5
7
f)
- 34
(-3)4
g)
280
16.
Circle the problem below for which the final answer would be undefined.
a)
-28 + 28
b)
5 + 30
5 + 30
-28 + 28
17.
Solve each of the following. Show all work using distributive property, addition
property and multiplication property where needed. Box your final answer.
a)
6x  5 + 9x = 7  4x  12
b)
2  3(5x + 2) = 2(3  5x)
c)
1.5(x  0.2) + 3 = 2.7x
d)
2
Y. Butterworth
/12
281
Take Home Final – Fall 2008
/3  1/3 x = 1/5 + 2/5 x
6
18.
Simplify the following polynomial problems.
a)
2(x + 3)  5x + 9(x  3) + 2
b)
(3x2 + 2x  0.8)  (0.1x2 + 5x  0.09)
19.
Evaluate the following using:
b)
(½ x  2/5) + (3/5 x  9)
x = 3, y = -2 and z = ½
If the problem involves fractions the final answer must be in fractions for full credit.
a)
x2  y
b)
x + (y  z)2
20.
Find the LCD for
2x2y3z & 3x3yz2
21.
Build the higher term for the following:
22.
Find the GCF of the terms and then factor the polynomial, rewriting as a product
of the GCF and a polynomial.
15x2y3z  18xy2z2 + 24x3y
c)
2
3x2y3
x + y
z2
= ________
18x3y3
Note: There are 3 questions I have not asked on this test that I will expect you to know
on the in-class portion of the final. Study for these:
a)
Adding & Subtracting Real Numbers (with Fractions & Decimals too)
b)
Sets of numbers: Real #’s, Integers, Rational #’s, Whole #’s & Natural #’s
c)
Properties of the real numbers
Y. Butterworth
Take Home Final – Fall 2008
7